We explain a form for the rainbow-ladder kernel whose momentum-dependence is consonant with modern DSE-and lattice-QCD results, and assess its capability as a tool in hadron physics. In every respect tested, this form produces results for observables that are at least equal to the best otherwise obtained in a comparable approach. Moreover, it enables the natural extraction of a monotonic running-coupling and -gluon-mass.

We introduce a method based on the chiral susceptibility, which enables one to draw a phase diagram in the chemical-potential/temperature plane for strongly-interacting quarks whose interactions are described by any reasonable gap equation, even if the diagrammatic content of the quark-gluon vertex is unknown. We locate a critical endpoint (CEP) at (µ E , T E ) ∼ (1.0, 0.9)Tc, where Tc is the critical temperature for chiral symmetry restoration at µ = 0; and find that a domain of phase coexistence opens at the CEP whose area increases as a confinement length-scale grows.

In principle, the strong-interaction sector of the Standard Model is characterised by a unique renormalisation-group-invariant (RGI) running interaction and a unique form for the dressed-gluonquark vertex, Γµ; but, whilst much has been learnt about the former, the latter is still obscure. In order to improve this situation, we use a RGI running-interaction that reconciles top-down and bottom-up analyses of the gauge sector in quantum chromodynamics (QCD) to compute dressedquark gap equation solutions with 1,660,000 distinct Ansätze for Γµ. Each one of the solutions is then tested for compatibility with three physical criteria and, remarkably, we find that merely 0.55% of the solutions survive the test. Evidently, even a small selection of observables places extremely tight bounds on the domain of realistic vertex Ansätze. This analysis and its results should prove useful in constraining insightful contemporary studies of QCD and hadronic phenomena.

Ground-state, radially-excited and exotic scalar-, vector-and flavoured-pseudoscalar-mesons are studied in rainbow-ladder truncation using an interaction kernel that is consonant with modern DSE-and lattice-QCD results. The inability of this truncation to provide realistic predictions for the masses of excited-and exotic-states is confirmed and explained. On the other hand, its application does provide information that is potentially useful when working beyond this leading-order truncation, e.g.: assisting with development of projection techniques that ease the computation of excited state properties; placing qualitative constraints on the long-range behaviour of the interaction kernel; and highlighting and illustrating some features of hadron observables that do not depend on details of the dynamics.

Lepton scattering is an established ideal tool for studying inner structure of small particles such as nucleons as well as nuclei. As a future high energy nuclear physics project, an Electron-ion collider in China (EicC) has been proposed. It will be constructed based on an upgraded heavy-ion accelerator, High Intensity heavy-ion Accelerator Facility (HIAF) which is currently under construction, together with a new electron ring. The proposed collider will provide highly polarized electrons (with a polarization of ∼80%) and protons (with a polarization of ∼70%) with variable center of mass energies from 15 to 20 GeV and the luminosity of (2–3) × 1033 cm−2 · s−1. Polarized deuterons and Helium-3, as well as unpolarized ion beams from Carbon to Uranium, will be also available at the EicC.The main foci of the EicC will be precision measurements of the structure of the nucleon in the sea quark region, including 3D tomography of nucleon; the partonic structure of nuclei and the parton interaction with the nuclear environment; the exotic states, especially those with heavy flavor quark contents. In addition, issues fundamental to understanding the origin of mass could be addressed by measurements of heavy quarkonia near-threshold production at the EicC. In order to achieve the above-mentioned physics goals, a hermetical detector system will be constructed with cutting-edge technologies.This document is the result of collective contributions and valuable inputs from experts across the globe. The EicC physics program complements the ongoing scientific programs at the Jefferson Laboratory and the future EIC project in the United States. The success of this project will also advance both nuclear and particle physics as well as accelerator and detector technology in China.

Understanding the origin and dynamics of hadron structure and in turn that of atomic nuclei is a central goal of nuclear physics. This challenge entails the questions of how does the roughly 1 GeV mass-scale that characterizes atomic nuclei appear; why does it have the observed value; and, enigmatically, why are the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD) abnormally light in comparison? In this perspective, we provide an analysis of the mass budget of the pion and proton in QCD; discuss the special role of the kaon, which lies near the boundary between dominance of strong and Higgs mass-generation mechanisms; and explain the need for a coherent effort in QCD phenomenology and continuum calculations, in exa-scale computing as provided by lattice QCD, and in experiments to make progress in understanding the origins of hadron masses and the distribution of that mass within them. We compare the unique capabilities foreseen at the electron-ion collider (EIC) with those at the hadron-electron ring accelerator (HERA), the arXiv:1907.08218v2 [nucl-ex] Rikutaro Yoshida (ryoshida@jlab.org) INTRODUCTIONAtomic nuclei lie at the core of everything we can see; and at the first level of approximation, their atomic weights are simply the sum of the masses of all the neutrons and protons (nucleons) they contain. Each nucleon has a mass m N ∼ 1 GeV, i.e. approximately 2000-times the electron mass. The Higgs boson produces the latter, but what produces the masses of the neutron and proton? This is the crux: the vast majority of the mass of a nucleon is lodged with the energy needed to hold quarks together inside it; and that is supposed to be explained by QCD, the strong-interaction piece within the Standard Model.QCD is unique. It is a fundamental theory with the capacity to sustain massless elementary degrees-of-freedom, viz. gluons and quarks; yet gluons and quarks are predicted to acquire mass dynamically [1][2][3], and nucleons and almost all other hadrons likewise, so that the only massless systems in QCD are its composite NG bosons [4,5], e.g. pions and kaons. Responsible for binding systems as diverse as atomic nuclei and neutron stars, the energy associated with the gluons and quarks within these Nambu-Goldstone (NG) modes is not readily apparent. This is in sharp and fascinating contrast with all other "everyday" hadronic bound states, viz. systems constituted from up = u, down = d, and/or strange = s quarks, which possess nuclear-size masses far in excess of anything that can directly be tied to the Higgs boson. 1

Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one-and two-body problems, which must be preserved in any veracious treatment of mesons as bound-states. In this connection, one may view the dressed gluon-quark vertex, Γ a µ , as fundamental. We use a novel representation of Γ a µ , in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quarkantiquark Bethe-Salpeter kernel, K , that is symmetry-consistent with a given quark gap equation.A strength of the scheme is its ability to expose and capitalise on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of H-diagrams in K , which are twoparticle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of Γ a µ in a Bethe-Salpeter kernel nor expressed as a member of the class of crossed-box diagrams. Thus, there are no general circumstances under which the WGT identities essential for a valid description of mesons can be preserved by a Bethe-Salpeter kernel obtained simply by dressing both gluon-quark vertices in a ladder-like truncation; and, moreover, adding any number of similarly-dressed crossed-box diagrams cannot improve the situation.

A symmetry-preserving truncation of the strong-interaction bound-state equations is used to calculate the spectrum of ground-state J = 1/2 + , 3/2 + (qq q )-baryons, where q, q , q ∈ {u, d, s, c, b}, their first positive-parity excitations and parity partners. Using two parameters, a description of the known spectrum of 39 such states is obtained, with a mean-absolute-relativedifference between calculation and experiment of 3.6(2.7)%. From this foundation, the framework is subsequently used to predict the masses of 90 states not yet seen empirically.Keywords Poincaré-covariant Faddeev equation · baryon spectrum · light and heavy quarks · Dyson-Schwinger equations · emergence of mass 1 IntroductionThe Faddeev equation was introduced almost sixty years ago [1]. It treats the quantum mechanical problem of three-bodies interacting via pairwise potentials by reducing it to a sum of three terms, each of which describes a solvable scattering problem in distinct two-body subsystems. The Faddeev formulation of that three-body problem has a unique solution.An analogous approach to the three-valence-quark (baryon) bound-state problem in quantum chromodynamics (QCD) was explained in Refs. [2][3][4][5][6]. In this case, owing to dynamical mass generation, expressed most simply in QCD's one-body Schwinger functions in the gauge [7][8][9][10][11][12][13][14][15][16][17][18] and matter sectors [19][20][21][22][23][24], and the importance of symmetries [25][26][27], one requires a Poincaré-covariant quantum field theory generalisation of the Faddeev equation. Like the Bethe-Salpeter equation for mesons, it is natural to consider such a Faddeev equation as one of the tower of QCD's Dyson-Schwinger equations (DSEs) [28], which are being used to develop a systematic, symmetry-preserving, continuum approach to the strong-interaction bound-state problem [29][30][31][32][33][34].The Poincaré-covariant Faddeev equation for baryons is typically treated in a quark-diquark approximation, where the diquark correlations are nonpointlike and dynamical [35]. This amounts to a simplified treatment of the scattering problem in the two-body subchannels (as explained, e.g. in Ref. [36], Sec. II.A.2), which is founded on an observation that the same interaction which describes